Research

Links to author profiles

My author profile on ZbMath, Orcid and Scopus.

Preprints

  • Amenable graphs and the spectral radius of extensions of Markov maps (with J. Jaerisch and E. Rocha). Preprint in arxiv.
  • Quasi-rigid operators and hyper-recurrence (with M. Saavedra). Submitted, preprint in arxiv.

Publications

  • Spectral triples and Dixmier trace representations of Gibbs measures: theory and examples (with L. Cioletti, L. Y. Hataishi, A. O. Lopes). Nonlinearity 37 (2024). Published version at doi, preprint in arxiv.
  • Minimal distance between random orbits (with S. Gouezel and J. Rousseau). Probability Theory and Related Fields (2024). Published version at doi, preprint in hal – archives ouvertes.
  • The Martin boundary of an extension by a hyperbolic group (with S. Bispo). Israel Journal of Mathematics 255 (2023), 1-62. published version, doi, arxiv.
  • Quenched and annealed equilibrium states for random Ruelle expanding maps and applications (with P. Varandas and X. Zhang). Ergodic Theory & Dynam. Systems 43 (2023), pp. 3150-3192 doi, arxiv. Published online 9/2022.
  • Invariant probabilities for discrete time linear dynamical systems via thermodynamic formalism (with A. Lopes, A. Messaoudi and V. Vargas). Nonlinearity 34 (2021), 8359-8391. doi, arxiv.
  • Thermodynamic formalism for random non-uniformly expanding maps (with S. Suzuki and P. Varandas). Communications in Math. Physics. 385 (2021), 369-427. doi, arxiv.
  • On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients (with X. Zhang). Nonlinearity 34 (2021), 1389-1407. doi, arxiv.
  • Ruelle Operator for Continuous Potentials and DLR-Gibbs Measures (with L. Cioletti and A. O. Lopes). Disc. Cont. Dyn. Sys. 40 (2020), 4625-4652. doi, arxiv.
  • Thermodynamic formalism for topological Markov chains on Borel standard spaces (with L. Cioletti and E. Silva). Disc. Cont. Dyn. Sys. 39 (2019) 6277-6298. doi, arxiv.
  • Spectral properties of the Ruelle operator for product type potentials on countable alphabets (with A. Lopes, L. Cioletti and M. Denker). Journal of the LMS 95 (2017) 684-704. doi, arxiv.
  • On the Lyapunov spectrum of relative transfer operators (with M. Bessa). Stochastics & Dynamics 16 (2016) 1650024-1 to 1650024-25. doi, arxiv.
  • Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps (with A. Lopes and B. Kloeckner). Nonlinearity 28 (2015) 4117-4137. doi, arxiv
  • Coupling methods for random topological Markov chains. Ergodic Theory & Dynam. Systems 37 (2017) 971–994. doi, arxiv, published online 2015.
  • Corrigendum to: Thermodynamic formalism for random countable Markov shifts (with M. Denker and Yu. Kifer). Disc. Cont. Dyn. Sys. 35 (2015), 593 – 594. doi, preprint.
  • Corrigendum and addendum to: On random topological Markov chains with big images and preimages.Stochastics & Dynamics 14 (2014).doi, preprint.
  • An extension of Kesten’s criterion for amenability to topological Markov chains. Advances in Mathematics 235 (2013) 450-468. doi, arxiv.
  • On random topological Markov chains with big images and preimages. Stochastics & Dynamics 10 (2010), 77-95. doi, arxiv.
  • Thermodynamic formalism for random countable Markov shifts (with M. Denker and Yu. Kifer). Disc. Cont. Dyn. Sys. 22 (2008), 131-164. doi.
  • Conservativity for random Markov fibred systems (with M. Denker and Yu. Kifer). Ergodic Theory & Dynamical Systems 28 (2008), 67-85.doi.
  • Lyapunov spectra for KMS states on Cuntz-Krieger algebras (with M. Kesseböhmer and B. O. Stratmann). Mathematische Zeitschrift 256(4) (2007), 871-893. doi, arxiv.
  • A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory (with B. O. Stratmann). Indagationes Mathematicae 17 (2006), 311 – 317. doi.
  • Infinite ergodic theory for Kleinian groups (with B. O. Stratmann). Ergodic theory & dynamical systems 25 (2005), 1305 – 1323. doi, Mathematica Gottingensis 10, 2003 (ps.gz).
  • The return sequence of the Bowen-Series map for punctured surfaces. Fundamenta Mathematicae 182 (2004), 221 – 240. doi.
  • The Bowen-Series map for some free groups. Mathematica Gottingensis 5, 2002 (ps.gz). PhD-thesis.

Articles in Proceedings

  • On conformal measures and harmonic functions. In the Proceedings of “New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo”, p. 275-304 (2019). Doi 10.1007/978-3-030-16833-9, arxiv.
  • Foreword (with Artur Lopes and Samuel Senti) of the Proceedings to the conference “Probability in Dynamics” in Rio de Janeiro 2014. Stochastics & Dynamics (2016).
  • On thermodynamic formalism for group extensions. Mini-Workshop: “Thermodynamic Formalism, Geometry and Stochastics”. Oberwolfach Reports 9 (2012), doi, extended abstract.
  • Semiconjugacies for skew products of interval maps (with M. Denker). RIMS Kokyuroku 1404 (2004). Preprint (Kyoto).

Proceedings

  • Editor (with Artur Lopes and Samuel Senti) of the Proceedings to the conference “Probability in Dynamics” in Rio de Janeiro 2014. Stochastics & Dynamics 16, Issue 2 and Issue 3 (2016).

PhD-Students

  • Elaine Rocha: Extensão do critério de Kesten sobre amenidade para extensões por grafos de aplicaçães Gibbs-Markov. Thesis defense: 9/2019.
  • Sara Ruth Pires Bispo: A fronteira de Martin de uma extensão por um grupo hiperbólico. Thesis defense: 11/2019.
  • Manuel Jesús Saavedra Jiménez: On recurrence of linear operators. Thesis defense: 9/2023.